Everyone agrees that the only serious way to keep people in their homes is through cramdowns. The problem with that is that this instantly demolishes the mark-to-myth assets that banks hold on their balance sheets. There's literally no way you can keep up the lie once the the principal on a mortgage has been written down.

So rather than push through a scheme like this, and make the banks take the hit, the GSEs (and by extension the Treasury, and by extension The Federal Reserve) takes the hit, leaving bank balance sheets intact.